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Examining the Impact of Neutral Theory on Genetic Algorithm Population Evolution

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Examining the Impact of Neutral Theory on Genetic Algorithm Population Evolution Examining the Impact of Neutral Theory on Genetic Algorithm Population Evolution Seamus Hill and Colm O’Riordan College of Engineering & Informatics, National University of Ireland Galway, Ireland Keywords: Neutral Theory, Genetic Drift, Neutrality, Genotype, Phenotype, Genetic Algorithms. Abstract: This paper examines the introduction of neutrality as proposed by Kimura (Kimura, 1968) into the genotype- phenotype mapping of a Genetic Algorithm (GA). The paper looks at the evolution of both a simple GA (SGA) and a multi-layered GA (MGA) incorporating a layered genotype-phenotype mapping based on the biological concepts of Transcription and Translation. Previous research in comparing GAs often use performance statis- tics; in this paper an analysis of population dynamics is used for comparison. Results illustrate that the MGA population’s evolution trajectory is quite different to that of the SGA population over dynamic landscapes and that the introduction of neutrality implicitly maintains genetic diversity within the population primarily through genetic drift in association with selection. 1 INTRODUCTION ated with a SGA and a multi-layeredGA (MGA). The motivation is to develop a tunable, synonymous, non- Neutral theory as proposed by Kimura (Kimura, trivial GA representation which incorporates neutral- 1968), offered an alternative to the Darwinian view; ity, in order to gain an understanding of the effects of stating that the mutations involved in the evolutionary neutrality on population dynamics. The contributions process are neither advantageous nor disadvantageous are as follows: an analysis of the impact of neutrality to the survival of an individual and that most muta- on population evolution; an examination of the im- tions are caused not by selection, but rather by random pact of neutrality on population variation; and finally genetic drift. However, in (Kimura, 1983), Kimura an illustration of the impact of neutrality on pheno- pointed out that although natural selection does play a typic variability. role in adaptive evolution, only a tiny fraction of DNA The paper is laid out as follows: Section 2 gives a changes are adaptive. The vast bulk of mutations are brief backgroundto Neutral theory and the use of neu- phenotypically silent. trality in GAs. Section 3 outlines the MGA used in By adopting the principal of Darwinism, simple the paper, while Section 4 describes the experiments genetic algorithms (SGA), can be viewed as imple- undertaken. Section 5 outlines and analyses the re- menting the process of evolution without containing sults, Section 6 concludes and Section 7 outlines fu- any explicit neutral mutations. In other words, each ture work. mutation is either an advantage or a disadvantage to the individual in terms of fitness, with selection then propagating the fitter individuals. As the search 2 BACKGROUND progresses, the exploration and exploitation ratio de- creases as the population converges. If we are to im- Neutral Theory as discussed by Kimura (Kimura, plement a genetic algorithm (GA) based on the prin- 1968), argues that mutation, not selection, is the main ciples of neutral theory then neutrality needs to be force in evolution. He describes how a mutation from introduced. Neutrality can be viewed as a situation one gene to another can be viewed as being neutral where a number of different genotypes can represent if it does not affect the phenotype, as the number of the same phenotype. Traditionally, GAs are evaluated different genotypes which store genetic information and compared in relation to performance measures. is far greater than the number of phenotypes. This In this paper, in addition to considering performance, implies that the representation from genotype to phe- the authors examine the population dynamics associ- notype must incorporate an element of redundancy 196 Hill, S. and O’Riordan, C.. Examining the Impact of Neutral Theory on Genetic Algorithm Population Evolution. In Proceedings of the 7th International Joint Conference on Computational Intelligence (IJCCI 2015) - Volume 1: ECTA, pages 196-203 ISBN: 978-989-758-157-1 Copyright c 2015 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved Examining the Impact of Neutral Theory on Genetic Algorithm Population Evolution and neutral mutations are possible. Mutations can be seen as relating to a collection. Variability, on be viewed as neutral if they change the genotype but the other hand, can be described as the leaning to don’t impact on the phenotype. vary and the “variability of a phenotypic trait de- Generally, neutrality can be viewed as a situation scribes the way in which it changes in response to where the size of the search space is increased, with- environmental and genetic influences” (Wagner and out an equivalent increase in the solution space. This Altenberg, 1996). When exploring the phenotypic results in a situation where a mutated individual, at space, it is critical to gain an understanding of the the genotypic level, can still represent the same phe- variational topology in trying to determine the shape notype. Neutrality should be beneficial when neutral- of the landscape (Toussaint, 2003b). Many evolu- ity changes the search bias in order to improve the tionary algorithms are created using a fixed variation probability of locating the global optimum. topology, in other words you don’t need to track the Although originally viewed as being anti- neutrality to explain the evolution trajectory. How- Darwinian, Kimura (Kimura, 1983) stated that al- ever, in nature, phenotypic variation landscapes are though natural selection is important in evolution, the not fixed. These non-fixed phenotypic variation land- number of DNA changes which are adapted in evo- scapes can be referred to as non-trivial in terms of lution are small, with the vast majority of mutations their genotype-phenotype map (Toussaint, 2003b). A being phenotypically silent. Following Kimura, work non-trivial genotype-phenotype map can be viewed by King and Dukes (King and Dukes, 1969) describes as having the following characteristics: firstly, a phe- how much of the evolution of proteins is down to neu- notype can be encoded by many genotypes and sec- tral mutations and genetic drift. A number of studies ondly, the phenotypic variability of a number of phe- focused on neutral theory (Schuster et al., 1994; Huy- notypes will depend on their genotypes (Toussaint, nen et al., 1996; Huynen, 1996; Schuster, 1997) etc. 2003a). and illustrated that by introducing redundant repre- sentation and thus, neutral mutation, the connectivity The primary inspiration for the multi-layered GA in fitness landscapes can be altered. In other words, can be found in the biological processes of transcrip- when a number of genotypes represent the same phe- tion and translation. At a very basic level, the bio- notype, they can be viewed as a neutral set and in turn logical process of transcription involves the copying alter the way in which a population explore the search of information stored in DNA into an RNA molecule, space. which is complementary to one strand of the DNA. Previous work on GA genotype-phenotype map- The process of translation then converts the RNA, us- pings which introduce neutrality, has produced results ing a predefined translation table, to manufacture pro- indicating the neutrality may prove useful in chang- teins by joining amino acids. These proteins can be ing environments and over more difficult landscapes. viewed as a manifestation of the genetic code con- Ebner et al. (Ebner et al., 2001) outlined how high tained within DNA and act as organic catalysts in levels of mutation could be sustained by having neu- anatomy. The MGA includes a layered genotype- tral networks present. They also identified that neutral phenotype map which adopts a basic interpretation networks assist in maintaining diversity in the popula- of the transcription and translation processes and al- tion, which may be advantageous in a changing envi- lows for the implementation of a missense mutation operator. The genotype search space is represented ronment. Similar findings were found in (Grefenstette l by Φg where Φg = 0,1 and l is the genotype and Cobb, 1993). Toussaint and Igel (Toussaint and { } Igel, 2002) argued that approaches to self-adaption in length. The transcription phase of the MGA maps Φ evolutionary algorithms can be viewed as an example the binary genotype to the DNA search space d, Φ l/2 of the benefits of neutrality, because with non-trivial where d = A,C,G,T , with the following map- pings: 00 {A; 01 C}; 10 G and 11 T . Fol- neutrality, different genotypes which are part of the → → → → same neutral set may have different phenotypic distri- lowing this, a bijective mapping takes place, map- ping the DNA space to an RNA space Φr, where butions. l/2 Φr = A,C,G,U . U is included for biological plausibility{ and has} no impact on the evolution un- less we include operators at this level. Following tran- 3 MULTI-LAYERED GENETIC scription, the translation phase takes place, mapping ALGORITHM (MGA) Φr Φp, where Φp represents the phenotype space → l/c and Φp = 0,1 , where c is the cardinality chosen The concepts of Variation and Variability need to be at initialisation{ } to create a translation table. The level differentiated. Variation can be described as the dif- of redundancy is determined by c and in this paper ference between individuals in a population and can c = 6 (see Figure 1), and implies Φg > Φp where | | | | 197 ECTA 2015 - 7th International Conference on Evolutionary Computation Theory and Applications c > 1. Missense mutationin natureis carriedout at the population will not enable the GA to locate the new RNA level. In relation to the MGA, the Missense mu- optimum. Hamming difference is used as a measure tation mapping is as follows: A U, C G, G A of diversity both for the genotypic and phenotypic and U C. To summarise the→ variation→ operators,→ diversity.
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